How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?

Step-by-step solution

We have the word 'D A U G H T E R' where vowels = A , U , E =3_ c ₂ consonant = D , G , H , T , R =5_ c ₃ There are 3_ c ₂ 5_ c ₃ =30 ways to select 2 vowels and 3 consonants 3_ c ₂ 5_ c ₃ =30 how each letter can be arranged in 5 ! ways 30 5 !=3600